The Magnetic Field and Impedances in Three-Phase Rectangular Busbars with a Finite Length

Abstract

The paper presents an analytical method for calculating impedances of rectangular bus ducts. The method is based on the partial inductance theory—in particular, the impedance of rectangular busbars in a three-phase system with a neutral conductor is described. The results of resistances and reactances of these systems of multiple rectangular conductors were obtained. Skin and proximity effects were taken into account. The measurements of the impedance of shielded and unshielded high-current busducts of rectangular conductors were also carried out. The magnetic field of the busbars was determined with several methods.

Practical Aspects of the Skin Effect in Low Frequencies in Rectangular Conductors

“…The results obtained from the application of the adopted method for analyzing the behavior of the skin and the proximity effects under power frequency presented themselves as being as relevant and coherent. At first, the analysis of the same theoretical case presented in [13] was successfully reproduced, which allowed not only calibrating the application of the proposed methodology as well as enabled its application to different cases with gradually increasing practicality, inspired in [10] and [31]. Thus, the case of two parallel bars with the electric field longitudinally applied in opposite directions was analyzed and showed how the skin effect and the proximity become somehow canceled, whereas the impedance of the so combined bars increases significantly.…”

“…For checking the applicability of the numerical method proposed in [13] for practical cases, based on a geometry proposed in [31] and inspired in [10], a commercially available panel bus bar was taken for running some laboratory tests.…”

Fast Numerical Model of Power Busbar Conductors Through the FFT and the Convolution Theorem

“…A particular type of distribution lines widely employed for electrical energy distribution are modular busbar systems [10], because they are fast and easy to install, modify and maintain [11]. As [10] states, high-current busbars with rectangular cross-section are often used in power substations and switching stations, with rated currents up to 10 kA and rated voltages in the range of 10-30 kV. Busbar systems consist of massive copper or aluminum rectangular conductors, which are subject to skin and proximity effects at the industrial frequency.…”

“…Different numerical methods have been proposed in the technical literature for obtaining the current density in rectangular conductors, taking into account both skin and proximity effects. On the one hand, analytical models of the bus bar conductors have been proposed in [11] for evaluating the electrodynamic forces in a bus bar system, in [23], using a far field/near field analysis, and in [10], using approximate triple integrals for obtaining the magnetic field produced by a threephase bus duct system. Nevertheless, these models are either approximated, or must be used in combination with numerical approaches, as for example in [15], [24], where the problem is formulated into a set of integral equations, which kernel is expressed analytically in the quasi-static regime, but the solution is found numerically using the method of moments (MoM).…”

“…impedance matrix for the system of conductors is obtained by forming appropriate row and column sums over the segment matrix, so that an explicit calculation of the segment currents is bypassed. The partial inductance approach has been applied also to the analysis of conductors in [10], [11], [13], [40]- [43]. Other methods, such as those based on induced voltage instead of partial inductances, have been also proposed recently [44].…”